Problem 44 - Algebra 1

Question

Evaluate the expression for the given value of x. $$4+x+10+(-10) ; x=3$$

Step-by-Step Solution

Answer

7

Step 1: Substitute x-value

Substitute 'x' with the given value, 3, into the expression. This leaves us with the problem: \[ 4+3+10+(-10) \]

Step 2: Perform Operations

Next, we perform the operations of addition and subtraction in the expression. The expression simplifies to: \[ 4 + 3 + 10 -10 = 7 \]

Step 3: Finalize Answer

As there are no more operations or variables, 7 is the result of the evaluation of the expression.

Key Concepts

Substitution

Substitution is a fundamental concept in algebra where you replace a variable with a specific value. This is often the first step in solving algebraic expressions. In the problem given, we are told to evaluate the expression \(4 + x + 10 + (-10)\) when \(x = 3\). By substituting \(x\) with 3, you transform the expression into \(4 + 3 + 10 + (-10)\).

• Why it's important: Substitution helps us evaluate expressions in terms of real numbers, making them easier to handle.
• How it works: Simply replace all instances of the variable with the given numerical value.
• Tip: Always double-check the substituted value to prevent any errors.

Try to visualize substitution as swapping out a placeholder letter with the number it represents. This step simplifies the arithmetic and guides you to find the value of the expression accurately.

Order of Operations

The order of operations is crucial when working with mathematical expressions. This guideline ensures that everyone calculates an expression the same way. The steps are typically remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). In our example \(4 + 3 + 10 + (-10)\), we primarily focus on addition and subtraction, which should be handled from left to right.

• Why use PEMDAS: It prevents ambiguity in mathematical expressions and ensures consistent results.
• Application: Even though our expression is simple, following the order of operations clarifies that the operations are performed sequentially.

In expressions that are more complex, apply the order of operations carefully for accurate results. Always keep this sequence in mind when calculating any algebraic expressions.

Arithmetic Operations

Arithmetic operations are the basic building blocks of mathematics that include addition, subtraction, multiplication, and division. Understanding these is essential for performing any calculations. In the expression \(4 + 3 + 10 + (-10)\), we see both addition and a subtraction implied by adding a negative number.

• Addition: Combine several numbers into a larger sum, as in \(4 + 3\).
• Subtraction: Simplifies certain numbers by removing their values from the total, here seen through the addition of \(-10\).
• Solution: Calculate step by step: first \(4 + 3 = 7\), then \(7 + 10 = 17\), and finally \(17 + (-10) = 7\).

These basic operations allow us to manipulate and solve expressions, making sense of numeric relationships. Mastering them ensures a solid foundation for more advanced mathematical concepts.